Module constrained 

Constrained optimization algorithms

This module provides methods for constrained optimization of scalar functions of one or more variables.

Example

use scirs2_core::ndarray::{array, Array1};
use scirs2_optimize::constrained::{minimize_constrained, Method, Constraint};

// Define a simple function to minimize: f(x) = (x[0] - 1)² + (x[1] - 2.5)²
// Unconstrained minimum is at (1.0, 2.5), but we add a constraint.
fn objective(x: &[f64]) -> f64 {
    (x[0] - 1.0).powi(2) + (x[1] - 2.5).powi(2)
}

// Define a constraint: x[0] + x[1] <= 3
// Written as g(x) >= 0, so: g(x) = 3 - x[0] - x[1]
fn constraint(x: &[f64]) -> f64 {
    3.0 - x[0] - x[1]  // Should be >= 0
}

// Minimize the function starting at [1.0, 1.0]
// Note: Initial point should be feasible (satisfy constraints) for best convergence
let initial_point = array![1.0, 1.0];
let constraints = vec![Constraint::new(constraint, Constraint::INEQUALITY)];

let result = minimize_constrained(
    objective,
    &initial_point,
    &constraints,
    Method::SLSQP,
    None
)?;

// The constrained minimum is at [0.75, 2.25] with f(x) = 0.125
// This is where the gradient of f is parallel to the constraint boundary,
// solved via Lagrange multipliers on x[0] + x[1] = 3.

Note: This function requires LAPACK libraries to be linked for certain optimization methods.

Re-exports

pub use augmented_lagrangian::minimize_augmented_lagrangian;

pub use augmented_lagrangian::minimize_equality_constrained;

pub use augmented_lagrangian::minimize_inequality_constrained;

pub use augmented_lagrangian::AugmentedLagrangianOptions;

pub use augmented_lagrangian::AugmentedLagrangianResult;

pub use cobyla::minimize_cobyla;

pub use interior_point::minimize_interior_point;

pub use interior_point::minimize_interior_point_constrained;

pub use interior_point::InteriorPointOptions;

pub use interior_point::InteriorPointResult;

pub use slsqp::minimize_slsqp;

pub use trust_constr::minimize_trust_constr;

pub use trust_constr::minimize_trust_constr_with_derivatives;

pub use trust_constr::GradientFn;

pub use trust_constr::HessianFn;

pub use trust_constr::HessianUpdate;

Modules

augmented_lagrangian

Augmented Lagrangian methods for constrained optimization

cobyla

COBYLA (Constrained Optimization BY Linear Approximations) algorithm

interior_point

Interior point methods for constrained optimization

slsqp

SLSQP (Sequential Least SQuares Programming) algorithm for constrained optimization

trust_constr

Trust-region algorithm for constrained optimization

Structs

Constraint

Constraint type for constrained optimization

Options

Options for the constrained optimizer.

Enums

ConstraintKind

The kind of constraint

Method

Optimization methods for constrained minimization.

Functions

minimize_constrained

Minimizes a scalar function of one or more variables with constraints.

Type Aliases

ConstraintFn

Type alias for constraint functions that take a slice of f64 and return f64